If the diameter of the base and curved surfaced area of a cylinder are 14cm and 352 cm²,respectively, then the total surface area of the cylinder is equal to:

The correct option is 660 cm².

Step 1: Identify the given values from the problem.
Diameter of the cylinder's base, $d=14\text{cm}$
Curved Surface Area (CSA) of the cylinder $=352{\text{cm}}^2$

Step 2: Find the radius of the base.
The radius ($r$) is half of the diameter:
$r=\frac{d}{2}=\frac{14}{2}=7\text{cm}$

Step 3: Understand the formula for Total Surface Area (TSA).
The Total Surface Area of a cylinder is the sum of its Curved Surface Area and the area of its two circular bases:
$\text{TSA}=\text{Curved Surface Area}+2\times \text{Area of base}$
$\text{TSA}=2\pi rh+2\pi r^2$

Step 4: Calculate the total area of the two circular bases.
Area of one base $=\pi r^2$
Area of two bases $=2\times \frac{22}{7}\times 7^2$
$=2\times \frac{22}{7}\times 49$
$=2\times 22\times 7$
$=308{\text{cm}}^2$

Step 5: Calculate the Total Surface Area (TSA).
$\text{TSA}=\text{CSA}+\text{Area of 2 bases}$
$\text{TSA}=352+308=660{\text{cm}}^2$

Thus, the total surface area of the cylinder is 660 cm².